Peter Romeo takes three of his greyhounds — rescued from racing — for a walk in Port Washington.Bloomberg

Three sleek greyhounds greet me at the train station in suburban Port Washington, New York. Attached to them is Peter Romeo, who is mostly undeterred by the tangle of leashes at his legs.

“Contrary to what everyone thinks, they are really not very hyper,” says Romeo, 54, who, with his wife Holly Klokis, 55, has turned their Long Island house into a modest shelter for greyhounds. “For the most part, they are extremely mellow and quiet.”

It’s true. The dogs show polite restraint, even in the excitement of a walk with a stranger. The even-tempered nature is a big plus since thousands of greyhounds are, like these three, racetrack retirees in need of a refuge.

The Humane Society of the US says the racing industry is responsible for overbreeding, which leads to too many unwanted dogs. Many of these natural runners suffer from confined living conditions. Others are cruelly destroyed.

According to the National Greyhound Association, about 20,000 find homes every year, most of them through the 300 or so adopting organizations across North America. These are usually retired racers or dogs bred for the track that never made the cut.

About 10 percent can’t find new owners, however, and many are euthanized every year. This is one reason why people like Romeo have opened their homes to the noble creature. That, and the greyhound’s congenial disposition.

“As soon as they are born they are handled, so they are very used to humans,” says Romeo. “They are extremely affectionate.”

When we arrive at the house, a fourth dog, Caesar, snoozes peacefully on the living-room floor. Caesar, who lost a leg to osteosarcoma, was Romeo’s first rescued greyhound 10 years ago. Adopters are often so smitten they come back for a second dog; some, like Romeo, don’t stop there. Now with four dogs (and four cats), the household has reached capacity.

Besides a permanent home for their own dogs, Romeo and Klokis also provide a temporary stopover for new retirees awaiting adoption. In the past three years they have shepherded 17 foster dogs to loving homes, networking with local groups Long Island GreyHound Transfer and Grateful Greyhounds, two nonprofits that help place retirees. Potential adopters are screened to make sure they are serious about their commitment, and that their dogs will have plenty of room to exercise but not too much.

“That’s one thing about greyhounds,” says Romeo. “You can’t let them run free because they run so far and so fast that they get lost.”

Said to be the oldest pure breed in existence, the greyhound was originally raised for hunting in the Middle East at least 4,000 years ago.

For large dogs, they are said to make excellent pets for city dwellers. They don’t bark much, and they are so used to living in crates from their days at the track, even a small studio will seem expansive to them.

There are no clear numbers on how many need new homes, but one thing is certain: Greyhound racing is disappearing in the US. With a stagnant economy and the popularity of racing waning, track owners are shutting their gates. The latest casualty is VictoryLand of Shorter, Ala., which stopped live racing in May.

“They want to save dollars, and we want to save dogs,” says Christine Dorchak, president and general counsel for Grey2k USA, a nonprofit group that advocates ending the racing industry altogether. Since she co-founded the organization in 2001, the number of states that allow racing has dropped to 7 from 15 (it’s outlawed in New York). Today there are only 25 tracks in country, more than half of them in Florida.